Evaluating Steiner-tree heuristics and diameter variations for application layer multicast

Latency reduction in distributed interactive applications has been studied intensively. Such applications may have stringent latency requirements and dynamic user groups. We focus on application-layer multicast with a centralized approach to the group management. The groups are organized in overlay networks that are created using graph algorithms that create a tree structure for the group. A tree has no cycles and uses a small routing table, as opposed to a connected overlay mesh. We investigate a group of spanning tree problems that are referred to as Steiner tree problems, and we have a particular focus on reducing the diameter of a tree, which is the maximum pairwise latency in a tree. In addition, we focus on reducing the time it takes to execute membership changes. In that context, we use coreselection heuristics to find well-placed client nodes, and edge-pruning algorithms to reduce the number of edges in an otherwise fully meshed overlay. Our edge-pruning algorithms strongly connect well-placed client nodes to the remaining group members, to create new and pruned group graphs. Consequently, when a tree algorithm is applied to a pruned group graph, it is manipulated into creating trees with a smaller diameter. We devised new Steiner-tree heuristics that reduced the diameter, and also proposed new edge-pruning algorithms to make the tree construction faster. These heuristics and algorithms were implemented and analyzed experimentally along with several spanning-tree and core-selection heuristics found in the literature. We found that a full-mesh of shortest paths makes it difficult for Steiner-tree heuristics to find better trees than spanning tree algorithms. The network seen from the application layer is in fact a full mesh of shortest paths. In addition, we found that faster Steiner-tree heuristics that do not explicitly optimize the diameter are able to compete with slower heuristics that do optimize it. Email address: knuthelv,griff,[email protected] (Knut-Helge Vik, P̊al Halvorsen, Carsten Griwodz). Preprint submitted to Elsevier 3 March 2008